Free vibration analysis of laminated and sandwich plates using quadrilateral element based on an improved zig-zag theory

Abstract

In this article, an improved zig-zag theory (ZIGT) is proposed for free vibration analysis of laminated composite plates. The proposed theory a priori satisfies the continuity conditions of transverse shear stresses at interfaces. Moreover, seven independent variables are only involved in displacement field. Compared to the early ZIGTs suffering from C¹ requirement in their finite element implementation, the advantage of the proposed theory is that the first derivative of transverse displacement has been eliminated from the in-plane displacement fields. Thus, the C⁰ shape functions are only required during its finite element implementation. Due to its C⁰ continuity requirements and low computational costs, the proposed theory is adequate to implement in commercial finite element codes. Based on the proposed ZIGT, a C⁰ conforming quadrilateral element is developed for free vibration analysis of laminated composite and sandwich plates. Numerical results show that the proposed element is able to accurately predict the natural frequencies of laminated composite plates and sandwich plates with soft core. However, the global higher-order theories as well as the first-order theory remarkably overestimate the natural frequencies of such structures.